Because a tomographic reconstruction is generally an under-determined problem, it produces a solution space (extended set of potential solutions) rather than a unique solution. Such a solution space will typically include (significant numbers of) “dud” solutions that are, for example, physically impossible and/or an inaccurate representation of the specimen under investigation. In order to “weed-out” such dud solutions from the solution space, the reconstruction procedure is generally subjected to one or more constraints, e.g. by discarding negative results and/or results that contain (certain types of) discontinuities, for instance.
A fundamental problem with tomographic imaging is the finite/bounded nature of the input set of images on which reconstruction is performed. More particularly, if said input set comprises large “voids” (e.g. collections of lines of sight for which there are no input images available, or only a sparse collection of input images), then this can lead to significant inaccuracies/limitations in the associated tomogram. Typically, of the theoretically possible 4π steradian (2π degree) angular extent of potential lines of sight relative to the specimen, one or more angular ranges are missing from the accumulated set of input images, e.g. due to a limited tilt range of the employed specimen holder, apparatus obscuration effects, etc. This is commonly referred to as the “missing wedge” problem. For lines of sight that have a relatively large elevation angle relative to the specimen, parts of the specimen image will be projected into regions that are not present in the reconstruction volume. This is commonly referred to as the “local tomography” effect. Apart from causing visible artifacts in the reconstructed tomogram, such effects also cause significant ill-posedness of the mathematical reconstruction problem, causing the resolution and fidelity of the resulting tomogram to be extremely sensitive to noise, with sub-optimal reconstructions as a result.
Although prior-art tomographic imaging techniques have produced tolerable results up to now, innovative alternatives to conventional approaches are needed and are disclosed below.